Three-dimensional Electron Gas Research Articles

Tetragonal symmetry in the electron gas.

Two transitions to localized charge density at intermediate and low densities are obtained for the three-dimensional (3D) electron gas in the deformable jellium. At very low densities, where the second transition occurs, the tetragonal structure is obtained. A discontinuity in the coupling parameter \ensuremath{\Gamma} appears at both transition points. The evolution of the charge density is obtained and it shows translational symmetry breaking. The function \ensuremath{\Gamma} and the ground-state energy obtained in this work are compared to values reported for 3D systems with linear and planar symmetries.

Coulomb coupling between two-dimensional and three-dimensional electron-gas layers: Influence on electrical transport.

Momentum and energy transfer is considered via the Coulomb interaction between two-dimensional (2D) and (3D) electron-gas layers separated by a distance l. A direct current driven through either of the layers induces a contactless current in the other layer. The case when a 3D electron gas drags a 2D electron gas is treated in detail. The friction force between the gases for a given current in the 3D gas is proportional to ${\mathit{Tscrl}}^{\mathrm{\ensuremath{-}}6}$lnscrl for scrl\ensuremath{\rightarrow}\ensuremath{\infty} and to ${\mathit{T}}^{2}$${\mathit{scrl}}^{\mathrm{\ensuremath{-}}5}$lnscrl for T\ensuremath{\rightarrow}0 and sufficiently large scrl. Good agreement is obtained between theory and recent experimental results pertaining to momentum transfer.

Evidence for a first-order correction to the Boltzmann conductivity of a disordered three-dimensional electron gas.

Analysis of data from several experimental groups on electron mobility in dense neutral gases from 3 to 300 K reveals the existence of a correction to the mobility arising from incoherent multiple scattering that is proportional to $\frac{1}{{\mathrm{kl}}_{o}}$. This correction overwhelms the traditionally used $\frac{1}{{({\mathrm{kl}}_{o})}^{2}}$ term arising from coherent backscattering and dominates the gas density dependence of the mobility of thermal electrons in helium. We also reanalyze Si:P data above the metal-insulator transition in terms of these incoherent scattering corrections.

Physics in less than three dimensions

Abstract An introduction is given to the methods of production and the properties of one-, two-, and three-dimensional electron gases. In two dimensions this includes the formation of electron solids (Wigner crystallization) and the quantum Hall effects and in one-dimension, the quantization of ballistic transport. The article ends with a short discussion of the applications of low-dimensional structures in electronic and optoelectronic systems.

The thermoelectric effect in a semiconductor superlattice in a non-quantized electric field

The thermoelectric effect in a semiconductor superlattice in a nonquantized electric field is investigated for electrons of the lowest miniband in the linear approximation of Del T. Analytical expressions for the thermopower and the heat conductivity coefficient are obtained as functions of the superlattice parameters Delta and d, temperature, concentration and electric field E. The results confirm the fact that depending on the relation between Delta and other characteristic energies of the carrier charge (kT, xi and h(cross)/ tau ) the carrier charges can behave either as a quasi-two-dimensional or as a three-dimensional electron gas. The prospect of using a superlattice as a good-quality and highly efficient thermoelement is also proposed.

Mutual drag of two- and three-dimensional electron gases: A collective-collisions approach.

In the recent paper by Laikhtman and Solomon [Phys. Rev. B 41, 9921 (1990)] a theoretical description of the mutual-drag effect of two- and three-dimensional electron gases in heterostructures was given. In this paper a different approach based upon the concept of collective collisions between electrons is suggested. The mutual drag of two two-dimensional gases is considered briefly.

Inelastic Coulomb scattering in a two-band picture and the temperature dependence of the resistivity.

A calculation of the inelastic lifetime and the resistivity resulting from Coulomb coupling of conduction (``s'') electrons to a narrow (``d'') band is given for both the regular and the pair-transfer interactions in the ballistic regime. It is shown that in all cases for overlapping bands the scattering rate and the resistivity behave as ${\mathit{T}}^{2}$ for a three-dimensional electron gas and as ${\mathit{T}}^{2}$ lnT at two dimensions. This is the same temperature dependence as found for Coulomb scattering in a single band, but its contribution to the resistivity does not necessitate umklapp processes. The result contradicts recent arguments leading to a linear temperature dependence in a two-band picture at two dimensions. The latter can be obtained when a small amount of scattering by defects is added, as known for the single-band case. It is argued that such a linear contribution to the temperature-dependent resistivity may be more pronounced in the two-band case. Experimental manifestations of the results are discussed.

The influence of a two- or three-dimensional electron gas in the emitter of resonant tunnelling structures

Magneto-tunnelling spectroscopy is used to investigate the electron dispersion curves in the quantum well of two double barrier resonant tunnelling structures which differ only in the nature of their emitter contacts (two- and three-dimensional). Reasons for the deviation from the expected parabolic behaviour are discussed.

Temperature dependence of short-range correlations in the homogeneous electron gas.

The temperature-dependent behavior of short-range correlations in a homogeneous three-dimensional electron gas at finite temperatures and finite degeneracies is presented. From the physical meaning of the pair distribution function for two electrons at the same location, one would expect a function which increases monotonically with the temperature. Instead, a decrease is found for small temperatures. This effect is investigated extensively within the framework of the random-phase approximation of static-local-field-corrected approaches. Moreover, by applying first-order perturbation theory the nonmonotonic behavior is proven to appear in the high-density limit also. Using a density-functional based model for short-range correlations, a physical interpretation is obtained. Finally, the results are discussed in a comprehensive way.

Nuclear magnetic resonance in the Condon domain state

Calculations of splittings of nuclear magnetic resonance (NMR) lines at diamagnetic phase transitions are carried out for a three-dimensional electron gas. There is a good agreement between the theory and the experimental results in silver. The size of the Condon domains and the width of the domain walls are estimated. Experimental results on the de Haas-van Alphen effect in silver are analyzed with the help of the temperature-magnetic-field diagram. The results of the analysis are in agreement with the NMR data. The NMR splitting in a two-dimensional electron gas due to Condon domains is calculated.

Perturbational analysis of plasmon decay in jellium

Plasmon damping in the three-dimensional homogeneous electron gas is investigated within second order perturbation theory for the density-density response function. The equivalence of several existing approaches that take into account lowest order two-pair excitations is shown explicitly. Finally, a complete Monte-Carlo analysis of the multi-dimensional integrals for the dielectric function is made for arbitrary densities.

Properties of the electron gas in a magnetic field and their implications for Thomas-Fermi type theories of matter

We discuss the energy density of the homogeneous three-dimensional electron gas in a magnetic field in the Hartree-Fock approximation and demonstrate that it exhibits a series of first-order phase transitions when new Landau levels begin to be populated. We investigate consequences of this behavior for Thomas-Fermi type theories of matter in magnetic fields, and show that within this approximation it leads to singular features in electron density profiles.

Density- and current-response of a quasi-two-dimensional electron gas

For a quasi-two-dimensional electron gas of a single quantum well, the density- and current-response is considered. Using a general relation between the density-response function and the components of the current-response tensor, it is possible to show analytically that the dispersion curves of all collective excitations of the density-response are only correct in the unretarded limit in contrast to the case of the homogeneous three-dimensional electron gas of an isotropic solid.

Mutual drag of two- and three-dimensional electron gases in heterostuctures.

Mutual drag of two-dimensional (2D) and 3D electron gases in GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As/GaAs heterostructures is considered. The main purpose of the paper is to explain the recent experiment of Solomon et al. [Phys. Rev. Lett. 63, 2508 (1989)] in which a current in the channel induced a current in the gate and the latter changed its sign when temperature decreased. It is shown that Coulomb mutual scattering gives rise to two mechanisms of the current induction. The first of them is the direct momentum transfer between the 2D and 3D electron gases and induces a current in the gate in the same direction as that in the channel. The second mechanism is connected with the presence of a temperature gradient in the channel due to the Peltier effect on the contacts. Energy exchange between the electron gases transfers the temperature gradient to the gate where it induces a thermocurrent in the direction opposite to the current in the channel. At high temperatures the temperature gradient in the gate is small because of efficient energy exchange between the 3D electron gas and the lattice so that the current due to the direct momentum transfer dominates. When temperature decreases, the number of phonons participating in scattering processes with 3D electrons drops off (the Bloch-Gr\"uneisen regime sets in), and the energy transferred from the 3D electron gas to the lattice decreases. As a result the thermocurrent dominates and the total current changes its sign. The theory explains the principal features of the experiment.

Self-consistent DFT calculations of electronic states in superlattices and quantum wells with arbitrary compositional and doping profiles

A method is described for the self-consistent computation of electronic states of semiconductor superlattices and MQWS with arbitrary compositional and doping profiles within effective mass theory and the envelope function approximation. Non-parabolicity of bulk bands is accounted for by means of the Hellmann-Feynman theorem. Many-body effects are included within local density functional theory; the exchange-correlation potentials obtained using the Tanatar-Ceperley and Ceperley-Alder correlation energies for the two-dimensional and three-dimensional electron gas, respectively, are compared.

Energy exchange between heterostructure layers by real-space electron transfer

Using Monte Carlo simulation we investigate electron transport in GaAs-n-AlxGa1−xAs heterostructure with high electric field applied parallel to the layer interface. Within a three-dimensional electron gas model we study the energy exchange between adjacent layers caused by real-space electron transfer (RSET). We have calculated an x-dependent electron temperature Te(x), with x being the distance from the interface, and distribution function f(kx,x), where kx is a wave-vector component perpendicular to the interface. Te(x) behavior clearly shows that the energy exchange between layers occurs: the electron temperature in the GaAs layer (high mobility—strong heating by field) is lower and that in the n-AlxGa1−xAs layer (low mobility—weak heating by field) is greater than the corresponding bulk values. A peculiar feature of the electron temperature x dependence is its abrupt change at the interface. We have shown that the presence of temperature step is necessary for the energy exchange due to RSET and it should be present in parallel transport simulations of three-dimensional electron gas where modulation doping of layers and smooth interfaces with abrupt potential barriers are considered. Compared to bulk distributions, the results for f(kx,x) are visibly influenced both by RSET and energy exchange. All numerical results are interpreted using simple general considerations. Finally, it is discussed that increased electron temperature in the n-AlxGa1−xAs layer can lead to more effective thermionic emission back to the GaAs layer, and thus increases the speed of the RSET oscillator.

Density of states for the lowest landau level of a three-dimensional disordered system

The density of states of a three-dimensional non-interacting electron gas under the influence of a white noise potential and a strong magnetic field is examined. It is shown that for the lowest Landau level the density of states may be obtained from the eigenvalue of an ordinary differential equation. The numerical results are compared with the density of states of a one-dimensional system with a white noise potential. For the Lifshitz tail the density of states is investigated by the instanton method.

Electron energy levels for a dense electron gas in parabolic GaAs/AlxGa1-xAs quantum wells.

Parabolic GaAs/${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As quantum-well structures have been developed as a means of producing a uniform three-dimensional electron gas. Calculations of the actual density profile and energy levels in the Hohenberg-Kohn-Sham local-density-functional approximation are presented for several values of electron sheet density in the well. These results verify the predicted uniformity of the electronic-charge-density distribution over the occupied portion of the well and give more quantitatively correct estimates of the Fermi level and subband energy separations than available previously.

Quasiparticle lifetime of excited carriers in a semiconductor superlattice.

The plasmon spectrum of a semiconductor superlattice with electronic minibands of finite width is intermediate between those of a three-dimensional electron-gas and a periodic array of two-dimensional electron-gas layers. Because the plasmon spectrum is a manifestation of dynamic screening, the quasiparticle self-energy in this system displays novel behavior. A form of the plasmon-pole approximation is used to evaluate the lifetime \ensuremath{\tau} of a quasiparticle with wave vector K=(k,${k}_{z}$). The threshold value ${k}_{c}$ of the parallel component of the wave vector at which the excited electron can begin to emit plasmons varies with ${k}_{z}$, being larger for smaller ${k}_{z}$. The rate of increase of ${\ensuremath{\tau}}^{\mathrm{\ensuremath{-}}1}$ above threshold is also larger for smaller ${k}_{z}$.

Diffusion of one- and two-dimensional hot electrons in semiconductor quantum-well structures at low temperatures

The diffusion of degenerate hot electrons moving one- and two-dimensionally in quantum-well structures is studied with the help of a semianalytic solution of the Boltzmann equation. The influence of the diffusion current on the distribution function is included. Numerical results are obtained for GaAs material parameters and a lattice temperature of 4.2 K, for fields at which background impurity scattering predominates in carrier momentum relaxation and deformation potential acoustic scattering dominates in carrier energy relaxation. Compared to the three-dimensional electron gas (3DEG) in the bulk material, the diffusion of the two-dimensional electron gas (2DEG) is found to be strongly anisotropic, the longitudinal-to-transverse diffusivity ratio increasing with the increased heating of the electron gas. The field-dependence of the diffusivity of the one-dimensional electron gas (1DEG) is shown to be less than that of the 2DEG but more than that of the 3DEG.